Is there anyway to change the rotation mode of multiple bones at once?
Here is a script that will change all the pose bone rotation mode to the value set for to_mode in this case 'XYZ' for XYZ Euler Rotation on the active (context) object.

import bpy
from bpy import context

to_mode = 'XYZ'
arm = context.object

for pb in arm.pose.bones:
    pb.rotation_mode = to_mode


Possibly more useful to use context.selected_pose_bones which will set the mode only for those pose bones selected.

import bpy
from bpy import context

to_mode = 'XYZ'

for pb in context.selected_pose_bones:
    pb.rotation_mode = to_mode